Pappas–Rapoport flatness conjecture for spin local models at parahoric level

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Let F/F0F/F_0 be a quadratic extension, let (V,ϕ)(V,\phi) be a symmetric space of dimension 2n+22n+2, and let I⊂[0,n]I\subset [0,n] be non-empty. Let \RMI±\RM^\pm_I be the spin local model over \COF\CO_F, and let \RMI±\loc\RM^{\pm\loc}_I be the schematic closure of its generic fiber in \RMI±\RM^\pm_I. Pappas–Rapoport's flatness conjecture. The spin local model \RMI±\RM^\pm_I is flat over \COF\CO_F. Equivalently, \RMI±=\RMI±\loc\RM^\pm_I=\RM^{\pm\loc}_I. The paper states that the schematic closure is identified with a Pappas–Zhu local model and has strong geometric properties, but the supplied parser status does not establish that the conjecture itself is resolved.

References

Primary source

Jie Yang, Ioannis Zachos and Zhihao Zhao, “On p-adic integral moduli schemes and local models for PEL type D”, arXiv:2602.23813 (2026).

Additional references

2 papers in this index state this conjecture (2025–2026). The statement above is taken from the most recent of them; the others are arXiv:2512.16646.

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